Background
The standard Landsat 8 products provided by the USGS EROS Center consist of
quantized and calibrated scaled Digital Numbers (DN) representing multispectral
image data acquired by both the Operational Land Imager (OLI) and Thermal
Infrared Sensor (TIRS).
The products are delivered in 16bit unsigned
integer format and can be rescaled to the Top Of Atmosphere (TOA) reflectance
and/or radiance using radiometric rescaling coefficients provided in the
product metadata file (MTL file), as briefly described below. The MTL file also
contains the thermal constants needed to convert TIRS data to the atsatellite
brightness temperature. Further details can be found in the LDCM Cal/Val
Algorithm Description Document and the Landsat 8 Science Users’ Handbook
available from the Landsat website (location coming soon).
Conversion to TOA Radiance
OLI and TIRS band data can be converted to TOA spectral radiance using the
radiance rescaling factors provided in the metadata file:
L_{λ} = M_{L}Q_{cal}
+ A_{L}
where:
L_{λ} = TOA spectral
radiance (Watts/( m2 * srad * μm))
M_{L} = Bandspecific multiplicative rescaling factor from the
metadata (RADIANCE_MULT_BAND_x, where x is the band number)
A_{L} = Bandspecific additive rescaling factor from the
metadata (RADIANCE_ADD_BAND_x, where x is the band number)
Q_{cal} = Quantized and calibrated standard product pixel
values (DN)
Conversion to TOA Reflectance
OLI band data can also be converted to TOA planetary reflectance using
reflectance rescaling coefficients provided in the product metadata file (MTL
file). The following equation is used to convert DN values to TOA reflectance
for OLI data as follows:
ρλ^{'} = M_{ρ}Q_{cal}
+ A_{ρ}
where:
ρλ^{'} = TOA planetary
reflectance, without correction for solar angle. Note that ρλ'
does not contain a correction for the sun angle.
M_{ρ} = Bandspecific multiplicative rescaling factor
from the metadata (REFLECTANCE_MULT_BAND_x, where x is the band number)
A_{ρ} = Bandspecific additive rescaling factor from the
metadata (REFLECTANCE_ADD_BAND_x, where x is the band number)
Q_{cal} = Quantized and calibrated standard product pixel
values (DN)
TOA reflectance with a correction for the sun
angle is then:
ρλ = 
ρλ^{'} 
= 
ρλ^{'} 
cos(θ_{SZ})

sin(θ_{SE})

where:
ρλ = TOA planetary
reflectance
θ_{SE} = Local sun elevation angle. The scene center sun
elevation angle in degrees is provided in the metadata (SUN_ELEVATION).
θ_{SZ} = Local solar zenith angle; θ_{SZ}
= 90°  θ_{SE}
For more accurate reflectance calculations,
per pixel solar angles could be used instead of the scene center solar angle,
but per pixel solar zenith angles are not currently provided with the Landsat 8
products.
Conversion to AtSatellite Brightness
Temperature
TIRS band data can be converted from spectral radiance to brightness
temperature using the thermal constants provided in the metadata file:
T = 

K_{2} 

ln( 
K_{1} 
+1) 

L_{λ} 
where:
T =
Atsatellite brightness temperature (K)
L_{λ}
= TOA spectral radiance (Watts/( m2 * srad * μm))
K_{1}
= Bandspecific thermal conversion constant from the metadata
(K1_CONSTANT_BAND_x, where x is the band number, 10 or 11)